FOTD -- February 10, 2003 (Rating 3) Fractal visionaries and enthusiasts: I named today's less-than-stellar image "Stuff" because it is a good illustration of the fragmented bits and pieces of something, or perhaps nothing, that I call fractal 'stuff'. This stuff is not material, since it has no physical basis; yet it is not a total abstraction, since it can easily be rendered and visualized. It is just 'stuff', and that is what I have always considered it. The exponent of Z in the generating formula is 1.559612. I chose this number because 1.559612^1.559612 almost equals 2. (1.559611 is closer.) This fact has little significance in the appearance of the resulting fractal, and was chosen on a whim. Luckily, the image renders in only a few minutes, for I could honestly rate it no higher than an abysmal 3. But it is still worth a quick glance. As always, the GIF file has been posted to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> While rummaging around in the attic yesterday, I came upon the dried-out remnants of a toy chemistry set that I had played with long ago and then grown tired of. I have no idea how it got there, for I have moved several times since I received it as a Christmas gift back in the years when I was filled with wonder and just discovering science. (I also had a toy microscope, a toy telescope, a toy weather station, an erector set that was supposed to build a walking robot, [I never managed to get the robot constructed.], and all the other goodies that boys who have decided to become scientists enjoy.) As fate would have it, I never became a 'scientist', whatever one of them is. I almost accidentally became involved in the printing trade and eventually became a graphic designer. But I have never lost that sense of scientific wonder. However, since those early years, I have become familiar with relativity and quantum theory. As a result, I now wonder more than anything else about the philosophical basis of science. Where I once wondered what the moon is made of, I now wonder if the physical world actually is an 'objective reality' or if 'reality' is an attribute we have invented for convenience and then bestowed upon the aggregate of our sensual impressions. And I wonder whether it makes a difference. The star Sirius is 8 light years away. When I was much younger, this meant that if something were to happen at this moment on that star, we would not know about it for 8 years, because it would take 8 years for the information to reach us. Then I became interested in relativity and found that there is no such thing as a universal present moment of time. The phrase 'at this moment on that star' has different meanings for different observers. Instead of thinking that our present moment of time now exists at the position of the star, but due to the finite speed of light, we on earth are seeing the star as it existed 8 years ago, we can just as accurately think that we are seeing the star as it presently exists and the actual time at the star is now 8 years in the future, and it will take us 8 years to reach that future time. So at this moment, what time actually exists on the star Sirius? The question cannot be answered. Time is relative. Asking such a question is like asking someone to find the center of the surface of a featureless sphere. All that can be said is that wherever a particular observer is located, that observer will find himself in his own private present moment of time. And what does this ambiguity of time mean to us in our everyday lives? It means nothing at all -- that is unless we begin traveling around our galactic vicinity at a velocity which is a sizeable percentage of the velocity of light. When (and if) this time comes, we will find ourselves faced with such present- day absurdities as having a twin who was born at the same time as ourselves, yet is 20 years older or younger. But when this happens, the absurdities will not be absurd at all. This relativistic situation might seen weird enough, but relativity at least leaves us with a real world, objectively out there to serve as a firm foundation for the science we have developed over thousands of years. This is more than quantum theory does when it brings into question the very existence of objective reality. With ample sun and a temperature of 41F 5C, the weather was quite pleasant here at F.C. on Sunday. Had the ground not been snow-covered, the dynamically fractal cats would have had a great day in the yard. As it was, they had a not-quite-as-great day on the porch, chasing the few sunbeams that are just beginning to reach there. Today is starting cloudy and colder, with on-and-off periods of light snow. The duo will not enjoy this. I'll enjoy the day better when I finish the work, and I will not finish until I resume it, so until next time, take care, and never lose that sense of wonder, but be careful what you wonder about. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Stuff {;time=a few minutes-SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.68446783504689930/-0.804007887280942\ 20/1008.977/1/-165/2.03941030729737349e-013 params=1.559612/0/64/0 float=y maxiter=1100 inside=0 logmap=71 periodicity=10 colors=000osiqujrwktyluzmsynrxnqwnpvnovnnuomtolsok\ sojroiqohppgppfopenpdmpcmpail`fiZcfY`cXY`VVYUSVTPS\ RLPQIMOFJNCGM9DK6AJ37I04J47J7AKADKDFKHILKLLNNMQQMU\ TzmVwlYuk`ojbhg`bd_VbZT`XV_WW`VY`TZaS`bRaaPcaOdaNe\ `Lg`Kh`Jj_Hk_Gm_FnZDpZCqZBsY9tY8uY7sW9rVAqUBpTCoSE\ nRFlPGkOHjNIiMKhLLgKMeINdHPcGQbFRaES`DTWMSRURMbRHj\ QDrQFsPHtPJuOLvONwNPxNRyNQxOQxPQwQPwRPwSPvTPvUOvVO\ uWOuXOuYNtZNt_Ns`MsaMsbMrcMrdLreLqfLqgLqhMrlMspOqo\ PonQnmRllSjkTijUgiVehWdgXbfY`eZ_d_Yc`XbY_ZVaWScSQe\ PNgLKiIIkEFmBCo7Aq4Gp9MpDSoHYoLcnQinUomYtmaoo_jpYf\ rWasUXtSTvQOwOKxMSmR_bVgTZoIbv8flCcbFaTJZKMYIOZGP_\ FQ`ERaFTbHUcIVdJWeKXfLYgMZhNZiO_jP`kQ`lRamSbnTboU`\ pV_qWZrX_sY`tZau_cv`cwacxbcycczcczcezcgzchzckzckzc\ lzclzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcm\ zcmzcmzcmzcmzcmzcmzcmzcmz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================